Assignment on Discrete Mathematics

Added on - 21 Apr 2020

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Showing pages 1 to 4 of 13 pages
DISCRETEMATHEMATICS
Table of ContentsTask - 4.1.........................................................................................................................................2Task – 4.2.........................................................................................................................................3Task - 4.3........................................................................................................................................3Task - 4.4.........................................................................................................................................4Task - 4.5.........................................................................................................................................4Task - 4.6.........................................................................................................................................5Task – 4.7.........................................................................................................................................6Task - 4.8.........................................................................................................................................7Task - 4.9.........................................................................................................................................8Task - 4.10.......................................................................................................................................8Task - 4.11.......................................................................................................................................92
Task - 4.1x(n) =cos (2πkn/N+π/4), n=0, to n=N-1X(0) =cos(2π(0)(0)/1 + π/4)=cos (2π(0) + π/4)=Cos(0 + π/4)=cos (π/4)x(0) =0.70710x(1) = cos(2πkn/N + π/4)=COS (2π(1)(1)/2 + π/4)=COS (2π/2 +π/4)=-0.70710x(2) = cos(2πkn/N + π/4)=cos(2π(2)(2)/3 + π/4)= cos(8π/3 + π/4)=-0.96590x(3) =cos (2πkn/N +π/4)=cos (2π(3)(3/4) +π/4)=cos (18π/4 +π/4)=-70670x(N-1) = cos(2π(n)(N-1)/n + π/4=cos (2πnN-2πnN + π/4)(a)x(n)={0.70710,-0.70710,-0.96590,-0.70670.......cos (2π(n)(N-1)/n +π/4}(b)||x||=0.707103
Task – 4.2X=[1,-1,1,-1](a)L-2 normX2=x12+........+x02|x|=k=1n|xk|2X2=112+122+....(1)n2(b)orthogonal1(-1,1,-1,1)-11(1,-1,1,-1)-11(-1,1,-1,1)-1(c)||x||=|1,-1,1,-1|4
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